scholarly journals Truncated euler polynomials

2018 ◽  
Vol 68 (3) ◽  
pp. 527-536 ◽  
Author(s):  
Takao Komatsu ◽  
Claudio Pita-Ruiz
Keyword(s):  
Bernoulli Polynomial ◽  
Euler Polynomial ◽  
Euler Polynomials

Abstract We define a truncated Euler polynomial Em,n(x) as a generalization of the classical Euler polynomial En(x). In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial.

scholarly journals New Generalized Apostol-Frobenius-Euler polynomials and their Matrix Approach

2021 ◽  
Vol 45 (03) ◽  
pp. 393-407
Author(s):  
MARÍA JOSÉ ORTEGA ◽  
WILLIAM RAMÍREZ ◽  
ALEJANDRO URIELES
Keyword(s):  
Polynomial Matrix ◽  
Product Formula ◽  
Euler Polynomial ◽  
Euler Polynomials ◽  
Matrix Approach ◽  
Pascal Matrix ◽  
Differential Properties ◽  
Euler Matrix

In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials ℋn[m−1,α](x; c,a; λ; u). We give some algebraic and differential properties, as well as, relationships between this polynomials class with other polynomials and numbers. We also, introduce the generalized Apostol-Frobenius-Euler polynomials matrix ????[m−1,α](x; c,a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix ????[m−1,α](c,a; λ; u), we deduce a product formula for ????[m−1,α](x; c,a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix ????[m−1,α](x; c,a; λ; u), which involving the generalized Pascal matrix.

scholarly journals Explicit formulas for Euler polynomials and Bernoulli numbers

2021 ◽  
Vol 27 (4) ◽  
pp. 80-89
Author(s):  
Laala Khaldi ◽  
◽  
Farid Bencherif ◽  
Miloud Mihoubi ◽  
◽  
...  
Keyword(s):  
Linear Combination ◽  
Bernoulli Numbers ◽  
Euler Polynomial ◽  
Euler Polynomials ◽  
Explicit Formulas ◽  
Fixed Integer

In this paper, we give several explicit formulas involving the n-th Euler polynomial E_{n}\left(x\right). For any fixed integer m\geq n, the obtained formulas follow by proving that E_{n}\left(x\right) can be written as a linear combination of the polynomials x^{n}, \left(x+r\right)^{n},\ldots, \left(x+rm\right)^{n}, with r\in \left \{1,-1,\frac{1}{2}\right\}. As consequence, some explicit formulas for Bernoulli numbers may be deduced.

scholarly journals Remarks on Sum of Products of (h,q)-Twisted Euler Polynomials and Numbers

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Hacer Ozden ◽  
Ismail Naci Cangul ◽  
Yilmaz Simsek
Keyword(s):  
Euler Polynomials ◽  
Euler Polynomials And Numbers ◽  
Sum Of Products

scholarly journals Quadratic symmetry of modified q-Euler polynomials

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
SangKi Choi ◽  
Taekyun Kim ◽  
Hyuck-In Kwon ◽  
Jongkyum Kwon
Keyword(s):  
Euler Polynomials

scholarly journals Some Identities Involving the Fubini Polynomials and Euler Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 300 ◽  
Author(s):  
Guohui Chen ◽  
Li Chen
Keyword(s):  
Power Series ◽  
Second Order ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Non Linear ◽  
Combinatorial Methods

In this paper, we first introduce a new second-order non-linear recursive polynomials U h , i ( x ) , and then use these recursive polynomials, the properties of the power series and the combinatorial methods to prove some identities involving the Fubini polynomials, Euler polynomials and Euler numbers.

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